I think this is a reasonable question; the choices of CPAN modules is overwhelming, and yet there are some modules that I use frequently.
use Getopt::Long; # I use this in all my programs
use Carp qw(cluck confess);
use Time::HiRes; # I wish this was Perl's default
use Win32; # When I need to call a Win32 DLL
use XML::LibXML; # Meets all my XML needs; See also XML::SemanticDif
+f
use LWP; # LWP & friends for web stuff
use Exporter; # For writing my own modules
use IO::Handle;
# Some less frequently used favorites
use Term::ANSIColor; # The world is better in color
use Socket; # When you need to do your own socket thing
use DateTime::Format::* # For date/time processing
I hope that helps.